Ecodynamics pp 319-332 | Cite as

Unstable Determinism in the Information Production Profile of an Epidemiological Time Series

  • F. Drepper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

The information production profile of a time series reveals the short term predictability as a function of certain dynamical patterns in the most recent past. It offers the possibility to distinguish deterministic phases of development from stochastic ones even in cases where the determinism is locally unstable or chaotic.

This new instrument for time series analysis of nonlinear dynamical systems has been applied to epidemiological data on measles cases in England and Wales. It is shown that there are phases of development within the two year cycle, where the deviations from periodicity are dominated by local instabilities of the underlying determinism.

Keywords

time series analysis nonlinear dynamics generalized Kolmogorov-Sinai entropy local divergence rate unstable determinism chaotic attractors epidemiological time series measles 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. Anderson R. M., Grenfell B. T. and May R. M., J. Hyg., Camb. 93 (1984)Google Scholar
  2. Brandstätter A. et al, Phys. Rev. Lett. 51 (1983) 1442CrossRefGoogle Scholar
  3. Cohen A. and Procaccia I., Phys. Rev. A 31 (1985) 1872CrossRefGoogle Scholar
  4. Drepper F., Analyse Chaotischer Dynamik: Ein Makroskop fur Vielkomponentensysteme, yearbook 1986–87 of the Kernforschungsanlage Jülich (GMBH), p.o. box 1913, D 5170 Jülich, FRGGoogle Scholar
  5. Drepper F., Determinism in the Information Production Profile of a Stock Market Index, in Fritsch B. and Keller J.U. (ed.s), Dissipative Structures in Integrated Systems, series ed.: Forschungsstelle für gesellschaftliche Entwicklung, Mannheim, Nomos Verlag 1987Google Scholar
  6. Grassberger P. (1986a), Estimating the Fractal Dimensions and Entropies of Strange Attractors, in Holden A.V. (ed.), Manchester Univ. Press 1986Google Scholar
  7. Grassberger P. (1986b), Nature 323, (Okt. 1986) 609CrossRefGoogle Scholar
  8. Grassberger P. and Procaccia I., Physica 9 D (1983a) 189Google Scholar
  9. Grassberger P. and Procaccia I., Phys. Rev A 28 (1983b) 2591CrossRefGoogle Scholar
  10. Kolmogorov A.N., Entropy per Unit of Time as a Metric Invariant of Automorphisms, Dokl. Akad.Google Scholar
  11. Nauk. SSSR 124 (1959) 754, Engl. summary in Math. Rev. 21, 2035Google Scholar
  12. Lorenz E.N., Deterministic Nonperiodic Flow, J. Atmos. Sci. 20 (1963) 130Google Scholar
  13. Packard N. et al., Phys. Rev. Lett. 45 (1980) 712CrossRefGoogle Scholar
  14. Ruelle D. and Takens F., On the Nature of Turbulence, Commun. Math. Phys. 20 (1971) 167Google Scholar
  15. Schaffer W. M., Olsen L. F., Truty G. L., Fulmer S. L. and Graser D. J., in Markus et al. (ed.s), From Chemical to Biological Organization, Springer, Berlin, 1987Google Scholar
  16. Sinai Ya. G., On the Concept of Entropy of a Dynamical System, Dokl. Akad. Nauk. SSSR 124 (1959) 768Google Scholar
  17. Shaw R., Z. Naturforsch. 36a (1981) 80–112Google Scholar
  18. Takens F., Lecture Notes in Math. 898, Springer, Heidelberg — New York, 1981Google Scholar
  19. Termonia Y., Phys. Rev. A 29 (1984) 1612CrossRefGoogle Scholar
  20. Theiler J., Phys. Rev. A 34 (1986) 2427CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • F. Drepper
    • 1
  1. 1.Programmgruppe Systemforschung und technologische EntwicklungKernforschungsanlage JülichJülichFed. Rep. of Germany

Personalised recommendations